In the Lifshitz formulation, the microscopic composition of a material is represented by its bulk dielectric response. Small changes in a dielectric response can result in substantial variations in the strength of vdW interactions. However, the relationship between these changes is complicated and often over-simplified in popular approaches. Three example systems are used to study the effects of material modifications, to characterize important system parameters, and to elucidate this commonly misunderstood relationship. Modification of example dielectric spectra at a particular frequency influences all terms in the Matsubara summation of the Hamaker coefficient. The terms most affected by the change are distributed doubly non-locally over all frequencies and not confined to terms near to modification. Thus, the possibility of eliminating vdW interactions by spectral variation at a narrow frequency range is very remote.

Orientational dependence of vdW interactions is generally attributed to the effects of anisotropies of body shapes and dielectric responses. In order to disentangle these effects, the angular dependencies for several systems displaying a range of anisotropies are examined and the effects of shape and material anisotropies are mutually isolated in detailed calculations. Shape anisotropy effects are shown to result in torques between arrays of cylinders that are surprisingly stronger than those between half-spaces, even for arrays constructed of isotropic material.

Full Lifshitz's calculations of vdW interactions, though complicated and lengthy, accurately capture important effects in mesoscale systems. The Gecko Hamaker open-science software and its accompanying open database of optical properties provide users with the accurate vdW calculations that are necessary for deliberate mesoscale design and construction. The Lifshitz formulation gives Gecko Hamaker the unique capability to address orientational degrees of freedom, allowing users to calculate torques and angular-dependencies. The large variety of calculations made possible by Gecko Hamaker provides insights into mesoscale interactions that were previously inaccessible to users, such as DNA-DNA interaction's dependence on base pair composition and the unusual non-monotonic interactions displayed by certain single-walled carbon nanotubes. This dissertation includes previously published coauthored material.

]]>We study the polyelectrolyte brush in monovalent salt using self-consistent-field- theory. We confirmed the step-function polymer profile in strong-stretched state. We examine the ion distribution and assure the trapping counterions by the brush. We also study the polyelectrolyte brush in divalent salt using explicit Donnan equi- librium and free energy minimization. We calculation the brush height and degree of ionization self-consistently as function divalent salt concentration. We explained the non-monotonic behavior of brush height versus salt concentration (observed in experiment) by charge reversal.

]]>Terrestrial noise is also an important factor in the recovery of any gravitational wave search. This work also details a series of studies that enable the characterization of ground motion local to the Advanced LIGO inteferometers and the ability of the installed active seismic isolation to mitigate it.

]]>In an effort to do so, our work has two main parts, one is to develop an efficient algorithm called population annealing Monte Carlo and the other is to explore the physics of spin glasses using thermal boundary conditions. We present a full characterization of the population annealing algorithm focusing on its equilibration properties and make a systematic comparison of population annealing with two well established simulation methods, parallel tempering Monte Carlo and simulated annealing Monte Carlo. We show numerically that population annealing is similar in performance to parallel tempering, each has its own strengths and weaknesses and both algorithms outperform simulated annealing in combinatorial optimization problems.

In thermal boundary conditions, all eight combinations of periodic vs antiperiodic boundary conditions in the three spatial directions appear in the ensemble with their respective Boltzmann weights, thus minimizing finite-size effects due to domain walls. With thermal boundary conditions and sample stiffness extrapolation, we show that our data is consistent with a two-state picture, not the RSB picture for the EA model. Thermal boundary conditions also provides an elegant way to study the phenomena of temperature chaos and bond chaos, and our results are again in agreement with the droplet/scaling scenario.

]]>We first study the optimal geometry of cohesive interactions in straight flexible tubes by considering two interaction potentials. We find filaments adopt a locally skewed configuration, associated with a twist angle. The interaction energy decreases with the twist angle and ground states are found to be twisted. For pair-wise interactions, we find a generic behavior in the profile of the cohesive energy where the geometry of close-packed double helices dictates the shape of the assembly. By considering the effect of bending energy we find a critical angle where twisting would be favorable and provide a prediction for carbon nano-tubes. Conversely, in the presence of non pair-wise interactions, we observe metastability for small twist deviations.

Next we explore the packing of curved filaments and their dependence on shape, range of cohesive binding and number of filaments. We study two packing motifs, N−plies and N−packs, where the latter is found to be generically favored as the stable ground state due to its ability to follow a hexagonal arrangement and the larger number of neighbors it can have.

Finally we study the self-assembly of a helical pairs focusing in the orientational dependence of the interactions. We develop a geometric model that describes the energetics of bundle formation, consisting of an optimal inter-filament spacing, a preferred parallel orientation and a preference for a prescribed helical shape. We find the system to be highly frustrated and present a phase diagram with three ground state configurations. We compute threshold values of attraction needed to form bound states and conclude that binding is determined by the shape of the filament. We propose a connection between the nature of interactions and the local geometry of the assembly via coupling constants, which we believe to be the strongest virtue of our model.

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